An alloy is to contain copper and zinc in the ratio 9:4. If quantity of copper is 24 kg, the quantity of zinc is -

Options

A. `10 2/3 kg`
B. `10 1/3 kg `
C. `9 2/3 kg `
D. `9 kg `

Answer

To find the quantity of zinc in the alloy, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The ratio of copper to zinc is given as 9:4. This means for every 9 parts of copper, there are 4 parts of zinc.

2. **Define Variables**: Let the quantity of copper be represented as \(9x\) and the quantity of zinc as \(4x\), where \(x\) is a common multiplier.

3. **Set Up the Equation**: We know from the problem that the quantity of copper is 24 kg. Therefore, we can set up the equation:
\[ 9x = 24 \]

4. **Solve for \(x\)**: To find \(x\), divide both sides of the equation by 9:
\[ x = \frac{24}{9} = \frac{8}{3} \]

5. **Calculate the Quantity of Zinc**: Now that we have \(x\), we can find the quantity of zinc:
\[ 4x = 4 \times \frac{8}{3} = \frac{32}{3} \text{ kg} \]

6. **Convert to Mixed Number**: The quantity of zinc can also be expressed as a mixed number:
\[ \frac{32}{3} = 10 \frac{2}{3} \text{ kg} \]

### Final Answer:
The quantity of zinc in the alloy is \(10 \frac{2}{3}\) kg.

---